We study percolation on random tessellations of the euclidian space. We proof the uniqueness of the infinite cluster and provide two frameworks, that imply the existence of a non-trivial phase-transition. We show that various classes of random tesselations fit into on of these frameworks. In the second part, we study the Boolean model. We give a new proof for the sharpness of the phase transition and solve the Ornstein-Zernike equation. This leads to new lower bounds for the critical intensity.